\boldmath Average $\cal H_2$ Performance and Maximal Parameter Perturbation Radius for Uncertain Systems

Abstract

In this paper, methods are presented for calculating the maximal parameter perturbation bounds under ${\cal H}_2$ performance constraints for a family of uncertain systems and for calculating the average ${\cal H}_2$ performance under such parameter variations. The uncertain systems are described by state space models with nonlinear (polynomial) dependencies on real uncertain parameters. All results obtained are based on necessary and sufficient conditions. As a special virtue of the approach, the proposed algorithms for stability analysis and for performance analysis turn out to have exactly the same algebraic structure. An example illustrates the results and the algorithms.